I imagine that at max-Q the Dragon will start its own motors to fly slightly faster than the booster (and move sideways). Suddenly the tip of the rocket will not be aerodynamic anymore. What will happen to the booster when Dragon detaches? Is it expected that it will disintegrate?

Don't know the answer, but... Max-Q will mean there's a lot of stress on the booster at the point of separation, but the booster is also somewhat overengineered (40% past max expected loads is required for human-rated vehicle, IIRC) and also certainly could perform an emergency MECO (as indeed it would probably do in a real abort situation), which would cause the load to drop pretty rapidly. I would not expect the booster to be destroyed at separation. That said, I don't know if they'll be able to land it, what with the second stage still being attached... very different center of gravity!
– CBHackingJun 30 at 21:30

3

Blue Origin’s New Shepard booster survived such test, but it is slower and sturdier. SpaceX might try to add some nose cone hidden in the Dragon trunk to help it survive but that is only a speculation.
– jkavalikJun 30 at 21:54

@CBHacking we also have to consider that first and second stage still contain a lot of fuel at that point. That would propbably make it impossible to land the booster either due to the landing burn or the landing legs not beeing strong enough. The only way I can see the booster landing is when the 1st stage continues to burn until the usual MECO and separate from the 2nd stage at that point. This would result in a somewhat normal trajectory.
– DaGrooveJul 25 at 6:24

While I don't know for sure whether the landing legs can support the weight of the partially-fueled booster, I'd actually be surprised if they couldn't; peak load at touchdown might be quite high if the "hoverslam" is even slightly inaccurate. It's true that a single-engine landing burn would probably be insufficient, and even triple-engine might not cut it, but the only limit on the number of engines used at landing is probably the TEA-TEB supply, and aborting around max-Q means they can skip the re-entry burn so that's at least three ignitions they wouldn't usually have.
– CBHackingJul 25 at 7:48